Simplify the following expression: $\dfrac{84a^3}{14a^5}$ You can assume $a \neq 0$.
Answer: $ \dfrac{84a^3}{14a^5} = \dfrac{84}{14} \cdot \dfrac{a^3}{a^5} $ To simplify $\frac{84}{14}$ , find the greatest common factor (GCD) of $84$ and $14$ $84 = 2 \cdot 2 \cdot 3 \cdot 7$ $14 = 2 \cdot 7$ $ \mbox{GCD}(84, 14) = 2 \cdot 7 = 14 $ $ \dfrac{84}{14} \cdot \dfrac{a^3}{a^5} = \dfrac{14 \cdot 6}{14 \cdot 1} \cdot \dfrac{a^3}{a^5} $ $\phantom{ \dfrac{84}{14} \cdot \dfrac{3}{5}} = 6 \cdot \dfrac{a^3}{a^5} $ $ \dfrac{a^3}{a^5} = \dfrac{a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a} = \dfrac{1}{a^2} $ $ 6 \cdot \dfrac{1}{a^2} = \dfrac{6}{a^2} $